public-keyencryptionanddigitalsignatures-預覽頁
【正文】 = 10 x 160 +1. – 6. The Public Key is KU={7,187}. – 7. The Private Key is KR={23,187}. RSA Example () ? Encryption Example – Let M = 88. – C = 887 mod 187. – Now, consider the following property of modular arithmetic: ? Xa+b mod n={(Xa mod n)(Xb mod n)}mod n. ? C={(884mod187)(882mod187)(881mod187)}mod187 ? C={132 x 77 x 88} mod 187 ? C = 11. RSA Example () ? Decryption Example – Let C = 11. – M = 1123 mod 187. – M={(111mod187)(112mod187)(114mod187) (118mod187) (118mod187)}mod187 ? M={11 x 121 x 55 x 33x 33} mod 187 ? M = 88. Attacks on RSA ? Brute forcetry all possible keys. – This means large keys need to be used, but implementations will have longer putation time. ? Factor n, into its prime factors (p and q.) – For n large, this is a hard problem.
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